The range of value of λ for which the circles x2+y2=4 and x2+y2−4λx+9=0 have two common tangents is
A
λ∈[−138,138]
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B
λ>138 or λ<−138
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C
1<λ<138
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D
none of these
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Solution
The correct option is Bλ>138 or λ<−138 C1(0,0) and r1=2 C2(2λ,0) and r2=√4λ2−9 Since, circles have two common tangents |r1−r2|<C1C2<|r1+r2| |2−√4λ2−9|<|2λ|<|2+√4λ2−9| ⇒λ>138 or λ<−138